3D Mobility Models and Analysis for UAVs

TL;DR

This paper introduces a flexible family of 3D mobility models for UAVs based on stochastic differential equations, capturing control mechanisms and environmental effects, with analytical solutions for position and connectivity.

Contribution

It develops a novel stochastic differential equation-based framework for UAV mobility modeling, including explicit control and environmental factors, with analytical steady state and connectivity results.

Findings

Derived steady state distributions for UAV position under various control models.

Provided closed-form solutions for Ornstein-Uhlenbeck and on-off control processes.

Analyzed UAV connectivity probability in Rayleigh fading environments.

Abstract

We present a flexible family of 3D mobility models suitable for unmanned aerial vehicles (UAV). Based on stochastic differential equations, the models offer a unique property of explicitly incorporating the mobility control mechanism and environmental perturbation, while enabling tractable steady state solutions for properties such as position and connectivity. Specifically, motivated by UAV flight data, for a symmetric mobility model with an arbitrary control mechanism, we derive the steady state distribution of the distance from the target position. We provide closed form expressions for the special cases of the Ornstein-Uhlenbeck (OU) process and on-off control (OC). We extend the model to incorporate imperfect positioning and asymmetric control. For a practically relevant scenario of partial symmetry (such as in the x-y plane), we present steady state position results for the OU control. Building on these results, we derive UAV connectivity probability results based on a SNR criterion in a Rayleigh fading environment.